Bifurcations

  • Miklós Farkas
Part of the Applied Mathematical Sciences book series (AMS, volume 104)

Abstract

In this chapter the emphasis will be on the “Andronov-Hopf bifurcation”, the generic mathematical model of the phenomenon how a real world system depending on a parameter is losing the stability of an equilibrium state as the parameter is varied, giving rise to small stable or unstable oscillations. This will be treated in Section 2; applications in population dynamics will be presented in Sections 3 and 4. In Section 1 the underlying theory of structural stability will be dealt with in a concise form. According to the general structure of this book this Section ought to go into the Appendix; however, in this last chapter it yields, probably, an easier reference standing at the start.

Keywords

Periodic Solution Periodic Orbit Equilibrium Point Homoclinic Orbit Centre Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Miklós Farkas
    • 1
  1. 1.Department of MathematicsBudapest University of TechnologyBudapestHungary

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